Guignard Qualifications and Stationary Conditions for Mathematical Programming with Nonsmooth Switching Constraints

نویسندگان
Gorgini Shabankareh, Fatemeh ID 1
Izadi, Javad ID 2
Fallahi, Kamal ID 3
Kanzi, Nader ID 4

1 Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran

2 Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran

3 Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran

4 Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran

doi
10.30473/coam.2021.60747.1176
چکیده

In this paper‎, ‎some constraint qualifications ‎of‎ the Guignard type are defined for optimization problems with continuously differentiable objective functions and locally Lipschitz switching constraints‎. ‎Then‎, ‎a new type of stationary condition‎, ‎named parametric stationary condition‎, ‎is presented for the problem‎, ‎and it is shown that all the stationarity conditions in various papers can be deduced from it‎. ‎This paper can be considered as an extension of a recent article (see Kanzow, et al.) to the nonsmooth case‎. ‎Finally‎, ‎the article ends with two important examples‎. ‎The results of the article are formulated according to Clark subdifferential and using nonsmooth analysis methods.

کلیدواژه‌ها
Constraint qualification‎, ‎Stationary conditions‎, ‎Optimality conditions‎, ‎Switching constraints